Partial Fractions: Refresh Memory on Integral of x/(1+x^2)

In summary, partial fractions are a mathematical technique used to decompose a rational function into simpler fractions, making it easier to solve integrals and better understand the behavior of these functions. To find the partial fraction decomposition of a rational function, the denominator must be factored into irreducible factors and coefficients are solved for. Refreshing our memory on the integral of x/(1+x^2) can help us understand the concept of partial fractions. While partial fractions can be used to solve certain types of integrals involving rational functions, they may not be applicable to all integrals.
  • #1
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Homework Statement


Need to refresh my memory :-S

Indefinite integral of x/(1+x^2) ..


Homework Equations





The Attempt at a Solution



Would I use partial fractions on that bad boy?
 
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  • #2
nevermind... substitution of u = 1+x^2 is easier.. :-)
 
  • #3
Partial fractions is not a viable candidate for this problem, since 1 + x2 is irreducible in polynomials with real coefficients.
 

1. What are partial fractions?

Partial fractions are a mathematical technique used to decompose a rational function into simpler fractions. This can be helpful in solving integrals and other mathematical problems.

2. Why do we need partial fractions?

Partial fractions allow us to break down complex rational functions into simpler components, making it easier to solve integrals and other mathematical problems. It can also help us to better understand the behavior of these functions.

3. How do you find the partial fraction decomposition of a rational function?

To find the partial fraction decomposition of a rational function, you first need to factor the denominator into its irreducible factors. Then, for each distinct factor, you set up a fraction with that factor as the denominator and an undetermined coefficient as the numerator. Finally, you solve for these coefficients by equating the original rational function to the sum of the partial fractions.

4. What is the purpose of refreshing our memory on the integral of x/(1+x^2)?

Integral of x/(1+x^2) is a common example used in teaching partial fractions. Refreshing our memory on this integral can help us better understand the concept of partial fractions and how they can be applied to solve integrals.

5. Can partial fractions be used to solve any type of integral?

Partial fractions can be used to solve certain types of integrals, specifically those involving rational functions. However, not all integrals can be solved using partial fractions, and other techniques may need to be used in those cases.

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